Estimation of reaction forces in high bar swinging

Reaction forces experienced by gymnasts swinging on the high bar may be determined indirectly using inverse dynamics analysis or may be measured using strain gauges. The accuracy of inverse dynamics analysis may be poor because of errors in the estimated inertia parameters and in the accelerations obtained from digitized data. On the other hand the use of strain gauges is not always possible in elite competition. This paper presents a method for estimating the reaction forces based on the linear displacements of the bar. The bar was modelled as a point mass attached to horizontal and vertical linear springs (obeying Hooke’s law) with stiffness coefficients determined from static loading. The stiffness coefficients of the bar were determined with three different tensions in the stabilizing cables of the high bar. A force and video analysis of backward giant circles was performed. Estimates for the reaction forces were obtained by multiplying the bar displacements from the video analysis by the stiffness coefficients determined from the static loadings. Comparisons were made between the estimated reaction forces and the reaction forces recorded using strain gauges attached to the high bar. Varying the tension in the stabilizing cables of the high bar did not effect the stiffness of the bar. Root mean squared differences between estimated and recorded reaction forces were on average within 99 N for three ‘regular’ and three ‘accelerated’ giant circles. This was less than 3.5% of the range of forces recorded. The bar displacement method was able to estimate the peak reaction forces to within 7% on average, which compares favourably with 24% reported by Gervais (1993) using inverse dynamics.     

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